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# help

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A belt and a wallet cost \$42 while 7 belts and 4 wallets cost \$213. Find the cost of a belt and a wallet.

Apr 10, 2020

#1
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"A belt and a wallet cost \$42"

I THINK you might want the cost of a wallet and the cost of a belt.

b + w = 42             b = 42-w    sub this into the following eq

7b + 4w = 213

7(42-w) + 4w = 213     solve for 'w'    then sub this value into one of the equations to solve for 'b'

Apr 10, 2020
edited by ElectricPavlov  Apr 10, 2020
#2
+240
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This can be written as a system of equations to solve.

Let b be the number of belts and w be the number of wallets.

b+w=42

7b+4w=213

Multiply the first equation by 4

4b+4w=168

Subtract this equation from the second.

(7b-4b)+(4w-4w)=213-168

The ws cancel out!

Now simplify.

3b=45

b=\$15

This can be substituted back into the first equation

15+w=42

Subtract 15

w=\$27

Double check to make sure these numbers work:

15+27=42, this one works

7(15)+4(27)=213 This one also works so this is the correct answer.

Apr 10, 2020